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Journal of Biogeography (J. Biogeogr.) (2008) 35, 711–723 ORIGINAL ARTICLE A topography-based model of forest cover at the alpine tree line in the tropical Andes Maaike Y. Bader* and Johan J.A. Ruijten Centre for Geo-Information, Wageningen University, PO Box 47, 6700 AA Wageningen, The Netherlands ABSTRACT Aim To present a method that assesses the influence of environmental variables, including climate, substrate, topography, and anthropogenic disturbances, on the distribution of Andean forest at the tree line, and to compare this forest distribution between areas. Location Sangay National Park, on the eastern slopes of the Andes in central Ecuador. Methods A logistic regression model was built using topographical variables and environmental indices, derived from a digital elevation model, to explain forest cover, derived from a Landsat ETM image, in a zone around the average tree line altitude. Results The model shows that after altitude, which can explain about 80% of forest cover, wetness has the next strongest effect (areas accumulating water, but also cold air, were devoid of forest, resulting in inverted tree lines), followed by eastness (western slopes had forest to higher altitudes). Application of the model in two nearby areas showed that the real tree line was lower than the predicted tree line in both areas, probably owing mainly to macroclimatic differences in one area, and partly also to human land use in the other. The locations with the largest deviations could be the focus of further research concerning human impacts on tree line vegetation. *Correspondence and present address: Maaike Y. Bader, University of Oldenburg, Institute of Biology and Environmental Sciences, Functional Ecology of Plants, PO Box 2503, 26111 Oldenburg, Germany. E-mail: [email protected]/ [email protected] Main conclusions The tree line is located at lower altitudes on east-facing slopes, which may be because high levels of radiation are received by east-facing slopes in the clear mornings, resulting in the photoinhibition of tree seedlings in the páramo. In spite of the limitations of the quality and resolution of the remote sensing data, the presented method provides indications for important ecological factors at the tree line. The method also allows the detection of differences in tree line position between areas, which may reflect climatic differences or the location of anthropogenic disturbances. Keywords Andes, cloud forest, digital elevation model, Ecuador, logistic regression model, páramo, remote sensing, Sangay National Park, topography. Alpine tree lines are conspicuous landscape boundaries on mountains worldwide (Körner & Paulsen, 2004). The tree line, as we use the term, is the transition from the uppermost closed forest to low alpine vegetation. The areal extents of these two ecosystems therefore depend strongly on the position of the tree line, which defines one of their altitudinal boundaries. The causes of the alpine tree line are not well understood, nor are the factors that determine its position in the landscape. Available warmth is generally assumed to be the main limitation for forest growth at the tree line (Körner, 1998), but locally other factors may determine the forest distribution, for example moisture availability, solar radiation, wind, snow cover, geomorphic processes, and human influence (Holtmeier & Broll, 2005). The spatial pattern of forest distribution should ª 2007 The Authors Journal compilation ª 2007 Blackwell Publishing Ltd www.blackwellpublishing.com/jbi doi:10.1111/j.1365-2699.2007.01818.x INTRODUCTION 711 M. Y. Bader and J. J. A. Ruijten reflect the important factors at a particular tree line and can therefore help us to understand what ecological processes are taking place. Most tropical mountains have long been inhabited by people, who may have lowered tree lines by forest clearance or by burning the alpine vegetation. Because of the widespread and long-standing human influence it is hard to determine which tree lines have been affected by humans and which have not, and what the natural tree line position would be. This results in controversies regarding the status of present tree lines and forest patches in the alpine zone (Ellenberg, 1979; Miehe & Miehe, 1994; Kessler, 2002) and regarding practical issues such as whether and where páramo areas should be (re-)forested (Fehse et al., 2002). In mountain regions, the topography is an important determinant of local conditions, including microclimate, soil properties, and disturbances (Brown, 1994). The use of topographic variables derived from a digital elevation model (DEM) as substitutes for field-measured environmental variables is becoming a common practice in the modelling of mountain vegetation (Brown, 1994; del Barrio et al., 1997; Hoersch et al., 2002; Dirnböck et al., 2003a; Hörsch, 2003; Van Niel et al., 2004). The advantage of using topography derived from a DEM as a substitute is that DEMs are spatially continuous and available without cost for the entire world (USGS, 2000), albeit not always at the required spatial scale. If direct climatic and other environmental data, such as climatestation and ground-survey data, are available, a DEM can be used to interpolate these point-data (Zimmermann & Kienast, 1999; Dirnböck et al., 2003b). Where no direct environmental data are available – as for most tropical mountains, including our study area – the spatial distribution and relative values of several ecologically relevant environmental variables can be derived using only a DEM. Most studies that relate mountain vegetation to topography are concerned with the European Alps (Zimmermann & Kienast, 1999; Guisan & Theurillat, 2000; Hoersch et al., 2002; Dirnböck et al., 2003a; Hörsch, 2003) or the Rocky Mountains (Brown, 1994; Allen & Walsh, 1996; Cairns, 2001). No such studies have been published for tropical mountains, although landslide hazards have been predicted based on topography in southern Ecuador (Brenning, 2005). Important climatic factors for forests at the tree line are temperature and solar radiation (Körner, 1998). These factors are strongly influenced by the topography, but in the tropics the effect of topography is different from that in temperate regions. For instance, in the tropics, north–south differences are less pronounced, whereas east–west differences may be larger than in temperate regions (Smith, 1977; Sarmiento, 1986), and patterns related to snow accumulation and movement are absent. Logistic regression models based on topography and other environmental factors have been used to predict vegetation types (Brown, 1994; Augustin et al., 2001; Virtanen et al., 2004; Calef et al., 2005; Maggini et al., 2006), species distributions (Zimmermann & Kienast, 1999; Robertson et al., 2003), animal habitats (Augustin et al., 1996) and landslide 712 hazards (Brenning, 2005). A large and growing number of alternative methods are available for predicting the distribution of species and communities (del Barrio et al., 1997; Augustin et al., 2001; Robertson et al., 2003; Austin, 2007), and some of these have been shown to perform better than logistic regression under certain conditions (Cairns, 2001; Elith et al., 2006). However, we have chosen to use the latter method because it is relatively simple and has already proved its value in many case studies (Robertson et al., 2003; Brenning, 2005). We used a logistic regression approach to describe the relationship between forest distribution at the tree line, and hence the position of the tree line itself, and mountain topography. The purpose of the model was twofold: (1) the identification of topographic variables and related environmental conditions and processes that are important for forest distribution; and (2) the comparison of forest distributions in areas that differ in terms of human disturbance, climate, or other factors. We show how a model developed for a natural tree line in central Ecuador helped to identify important factors affecting forest distribution and tree line position. This model was then applied in two nearby tree line areas, one that is presumably undisturbed and another that is known to be influenced by humans. METHODS Study area The three study areas (one for model development and crossvalidation, and two for model application) are situated in central Ecuador on the eastern Cordillera of the Andes in Sangay National Park (Fig. 1). On this Cordillera, the westoriented, inter-Andean watersheds are mostly devoid of forest, owing to human land use, and are not included in the study areas. The east-oriented watersheds have forested slopes, stretching from the tree line down to the Amazonian lowland forests. Generally, the vegetation belts on the Amazonian side occur at lower elevations than those on the inter-Andean side, because of the higher cloudiness and resulting lower temperatures on the Amazonian side (Bendix & Rafiqpoor, 2001; Sklenář & Laegaard, 2003; Bendix et al., 2006a). The following description is based on our field observations in the area near Atillo and existing literature about this park (Armstrong & Macey, 1979; Mena et al., 1997; Downer, 2001; UNEP-WCMC, 2003). The study areas have a typical tropical alpine climate, with low average temperatures and little annual variation but strong diurnal fluctuations (Sarmiento, 1986). Precipitation is high year-round. There is a relatively dry season from October to February in nearby Atillo, but this seasonality varies between locations and is expected to be less pronounced on the Amazonian side, where the study areas are located (Bendix & Lauer, 1992; Mena et al., 1997). Soils are deep humic andosols that have developed in volcanic ashes of various ages. The topography is generally steep, with U-shaped glacial valleys above c. 3000 m and V-shaped river valleys in the lower parts. Journal of Biogeography 35, 711–723 ª 2007 The Authors. Journal compilation ª 2007 Blackwell Publishing Ltd A topography-based tree line model Figure 1 Location of the study areas in Ecuador and in Sangay National Park. Grey shading indicates altitude: on the inset map of NW South America, darker shades represent higher altitudes; on the main map, darker shades represent lower altitudes. Elevation data: inset, GTOPO30 (USGS, 1996); main map, SRTM (USGS, 2000). The alpine vegetation (páramo) is dominated by tussock grasses (Calamagrostis spp., Festuca spp.) interspersed with various shrubs and herbs. Some wetter and undisturbed páramos are dominated by a tall reed-like bamboo (Neurolepis aristata (Munro) Hitchc.). The forest is an upper-montane cloud forest, which is characterized by low-stature trees with small sclerophyllous leaves and high epiphyte cover, especially bryophytes. Tree species richness is low compared with that of tropical lowland forests (Gentry, 1995), but high compared with that of temperate montane forests. The highest parts of the cloud forests are dwarf forests dominated by the tree species Escallonia myrtilloides L.F. and Gynoxys buxifolia (Kunth) Cass., in association with various Ericaceae, Neurolepis aristata, and possibly other trees or shrubs such as Diplostephium, Brachyotum, Hesperomeles, Buddleja, and Miconia (Fig. 2). The three study areas were selected based on the quality of the data (cloud-free images needed) and the level of human influence expected. Within the square areas shown in Fig. 1, the forest distribution was modelled only in an altitudinal zone around the tree line in the east-oriented watersheds. The first area, used for the development of the model (training and Figure 2 Photo of the tree line in test area B, in Sangay National Park near Atillo. cross-validation area), is located north of Sangay volcano and is about 25 · 25 km in size (NW corner: 78º29¢ W, 01º46¢ S). It is about 6 h walk from the nearest village (Alao, c. 5000 inhabitants) to the closest point of this area. Human influence is restricted to extensive cattle grazing and some hunting. Journal of Biogeography 35, 711–723 ª 2007 The Authors. Journal compilation ª 2007 Blackwell Publishing Ltd 713 M. Y. Bader and J. J. A. Ruijten Burning is commonly associated with grazing in the Andes, but no evidence of widespread fires was identified. The second area, used for application of the model (test area A), is located north of the training area, east of El Altar volcano, and is about 25 · 25 km in size (NW corner: 78º27¢ W, 01º33¢ S). This area is very remote and is expected to experience little to no human influence. The Landsat image of this area has some cloud cover, meaning that some parts of the tree line are excluded from the application. The third area, also used for application of the model (test area B), is located south of the training area, about one hour’s walk from the village of Atillo (c. 400 inhabitants in 1986; UNEP-WCMC, 2003) to the closest point, and is about 30 · 30 km in size (NW corner: 78º35¢ W, 02º04¢ S). The people of Atillo cultivate potatoes and graze cattle and sheep in a broad glacial valley that is part of a west-oriented watershed (not included in the study area). Cattle grazing and the associated burning of the páramo vegetation are extended to the mountains around, including parts of the National Park. Another, similar village (Ozogoche) is also situated close to the study area. Human influence is expected to decrease with distance to these villages. A gravel road connecting Guamote in the inter-Andean valley to Macas in the Amazon lowlands, via Atillo, has recently been established here and is expected to have a strong environmental impact in the region (UNESCO, 1999) (Fig. 2). Data The data used were a Landsat Enhanced Thematic Mapper (ETM) image from NASA’s Global Orthorectified Landsat Data Set (Tucker et al., 2004) and a DEM produced by the Shuttle Radar Topography Mission (SRTM) (USGS, 2003). The Landsat image had a resolution of 28.5 m; the DEM had a resolution of 90 m. These spatial resolutions determined the scale at which the analysis was carried out, and the types of patterns and processes that could be distinguished. Both the Landsat image and the DEM were geo-referenced by the supplier. The elevation values of the DEM were rounded to integers, resulting in 1-m intervals (USGS, 2000; GLCF, 2006). The reported spatial accuracies of the orthorectified data were < 50 m root mean square error for the Landsat data (Tucker et al., 2004), and < 9 m geolocation error and < 6 m height error for 90% of the SRTM DEM (Rodriguez et al., 2005). However, because of the strong relief, errors could be much larger for our study areas than was apparent from these global quality assessments (Jarvis et al., 2004; Falorni et al., 2005). Such inaccuracies will negatively affect the predictive power of logistic regression models (Van Niel et al., 2004). Data preparation The DEM had some missing values over land and negative values over water bodies, and it contained terraces, probably caused by the rounding of elevation values in the preprocessing by the provider (Wood, 2003). These ‘bad values’ and terraces were removed by creating elevation contour lines from the DEM and subsequently creating a hydrologically correct DEM from these contour lines (Hutchinson, 1989). This method is preferred over simpler filtering methods because the hydrologically correct DEM is more useful for the topographical analysis. The DEM was used to derive the following topographic variables and environmental indices: slope angle, aspect (eastness and northness), plan curvature, profile curvature, wetness index (CTI), solar radiation index (PRR), and erosion index (STCI) (Table 1, Fig. 3). The variables were derived at the original resolution of the DEM (90 m) and then resampled to 28.5 m, using bilinear interpolation, to match the resolution of the Landsat image. The position of the tree line was extracted from the Landsat image and used to define a tree line zone, within which the model was developed. This zone was used in order to exclude altitudes outside the range of the tree line. The forest area, including dwarf forest, was identified using supervised classification with a flexible probability threshold. Small clusters of forest and non-forest pixels (£ 4 pixels: covering less than half a SRTM pixel) were considered noise and were removed, both Table 1 Topographic variables and environmental indices used as independent variables in the logistic regression. Variable Description Altitude Slope Eastness Northness Plan curvature Profile curvature CTI PRRà STCI§ Altitude above sea level (m) Slope angle (degrees) Aspect east)west (1 to )1) Aspect north)south (1 to )1) Curvature perpendicular to slope Curvature in slope direction Compound topographic index Potential relative radiation Sediment transport capacity index Calculation Ecological meaning sin(aspect) cos(aspect) )1 = concave, 1 = convex )1 = convex, 1 = concave ln( As/tan b)* Hourly shaded relief (As/22.13)0.6/(sin b/0.0896)1.3* Temperature, moisture, CO2 pressure Solar radiation, stability, erosion, moisture Morning/afternoon solar radiation, wind, moisture Summer/winter solar radiation Solar radiation, wind, moisture, erosion/deposition Moisture, erosion/deposition Moisture, water logging, cold-air ponding Solar radiation potential Erosion potential *As: contributing area, derived with D¥ algorithm (Tarboton, 1997), b: local slope angle. Schmidt & Persson (2003). àPierce et al. (2005). §Moore et al. (1993). 714 Journal of Biogeography 35, 711–723 ª 2007 The Authors. Journal compilation ª 2007 Blackwell Publishing Ltd A topography-based tree line model Slope angle Altitude 51.4 6257 m N N 1564 m 0.0 Border tree line zone Border tree line zone Eastness Northness 1 (East) 1 (North) N N –1 (West) –1 (South) Border tree line zone Border tree line zone Profile curvature Plain curvature 0.65 0.68 N –0.55 N –0.64 Border tree line zone Border tree line zone PRR CTI 2.24 21.53 N N 1.55 4.54 Border tree line zone Border tree line zone STCI Figure 3 Distribution of the topographic variables and environmental indices in the training and cross-validation area. The legends refer to the lighter area within the border of the tree line zone. Note that the scales of plan and profile curvatures have opposite meanings. 350 N 0 Border tree line zone because their classification is likely to be incorrect, and because such small features could not be related to the coarser-scaled SRTM DEM. The classified image was converted to a vector format, where the boundaries between forest and non-forest were represented as lines. These lines were converted back to a grid format with the original pixel size (28.5 m). The overlay of this gridded line with the DEM (resampled to 28.5 m) gave us the altitude of all forest boundaries. To exclude forest boundaries not related to the altitudinal tree line, we excluded altitudes below 3300 m. From the remaining boundaries the average altitude was calculated, as well as the standard deviation. We then defined the tree line zone as the average tree line altitude ± two standard deviations (namely 3634 ± 2*185 m). This implies that approximately 95% of the tree line is included in the zone. Within this zone, the distribution of forest/non-forest was the subject of investigation. Journal of Biogeography 35, 711–723 ª 2007 The Authors. Journal compilation ª 2007 Blackwell Publishing Ltd 715 M. Y. Bader and J. J. A. Ruijten We used a combination of IDL ENVI (RSI/ITT, Boulder, CO, USA) and ArcGIS 9 (ESRI, Redlands, CA, USA) for the preparation of the data. Logistic regression A logistic regression model was built to predict the forest/nonforest distribution based on the topographic variables and environmental indices (Brenning, 2005). A logistic regression model predicts the probability that a pixel is covered by forest as follows: PðforestÞ ¼ eðaþb1 X 1 þb2 X 2 þþbn X n Þ 1 þ eðaþb1 X 1 þb2 X 2 þþbn X n Þ Model application where a and b1,…,n are the model coefficients for the constant and the topographic variables X1,…,n. Only half of the first study area was used for building the model (training area), and the other half was used for crossvalidation (cross-validation area). The area was divided into these two halves following a checkerboard pattern with 1-km squares (see Fig. 5a below). For the regression, the spss (SPSS Inc., Chicago, IL, USA) procedure ‘binary logistic regression’ was used with the forward stepwise algorithm based on a maximum-likelihood ratio test (Hosmer & Lemeshow, 1989). There was multicollinearity (bivariate or multivariate correlation) between some of the explanatory variables, as shown by high variance inflation factors for slope (10.0), PRR (6.0), CTI (4.5) and STCI (2.5). Multicollinearity complicates the assessment of the effects of the correlated variables in the model, but it does not affect the predictive power of the model (Garson, 1998). Multicollinearity can be handled either by leaving out the most correlated variables, or by combining variables into principal components (Brown, 1994; Baker & Weisberg, 1997; Garson, 1998; Cairns, 2001; SSTARS, 2005). However, when variables are combined into principal components the role of the individual variables becomes unclear, so we chose not to apply this method. Instead, we constructed separate models including only one of the correlated variables in each, and we interpreted the ecological effects of these variables from these stripped models. Spatial autocorrelation can be included in regression models to account for patterns that result from purely spatial processes, such as seed dispersal or herding behaviour (Augustin et al., 1996). At the scale of our data, however, we expected similarity between neighbouring points to be caused mainly by the similar topographical position, and not by purely spatial processes. We therefore chose not to include a spatial autocorrelation term in our model. However, spatial autocorrelation also implies that the data are not independent. Spatial dependence between data points will cause a false increase in the statistical significance of the model coefficients (Garson, 1998; Dalthorp, 2004; Brenning, 2005; Maggini et al., 2006). A possible solution to this problem is to build the model with a subsample of points, thereby increasing the distance and decreasing the correlation between points (Brown, 1994; Brenning, 2005). With this solution, 716 though, a lot of information is not used. We therefore chose to use all data points and to treat the reported significance of the model and model coefficients with extra caution. The model was applied to the held-back half of the checkerboard for cross-validation. The overall predictive accuracy of the model was determined by comparing the predicted forest cover, using the threshold P(forest) > 0.5, with the actual cover as derived from the Landsat image. The number of correctly predicted pixels for each class, as shown in a classification table, was used to calculate the overall predictive accuracy. The model was applied to test areas A and B, in a tree line zone with the same altitudinal limits as those in the training area (3264–4044 m a.s.l.). Apart from calculating the overall predictive accuracy for each area, we visually inspected the shape and locations of the deviations between the actual and the predicted cover. We also trained logistic regression models on the test areas, using the methodology described above, to see if the same topographic factors were important in these areas. RESULTS Importance of variables in the model Eight of the nine topographic variables contributed significantly to the logistic regression model (the complete model); only profile curvature was excluded (Table 2). The included variables contributed significantly to the model according to all statistics (Wald, change in )2 log likelihood, Akaike information criterion). However, the predictive accuracy of the model, Table 2 Results of a forward stepwise logistic regression including all the independent variables (the complete model). Significance of all variables: P < 0.001. The only variable not included in the model is profile curvature. The variables that have considerable effects on the models are printed in bold. The last column is the change in )2 log likelihood if the variable is removed from the model. The total model chi-square is 79699, Nagelkerke’s R2 is 0.633, and the predictive accuracy is 84.0%. Variable Model co-efficient SE Wald Altitude Eastness CTI Slope Northness STCI PRR Plan Constant )0.01312 )0.75409 )0.50856 0.06243 )0.24279 0.00701 3.19912 )0.95959 42.69393 0.00007 0.01332 0.00978 0.00281 0.01311 0.00041 0.20847 0.10560 0.56869 33185.48 3207.19 2701.91 494.70 343.06 290.06 235.49 82.57 5636.22 Change in )2 log likelihood 75950.79 3401.21 3001.21 498.68 345.18 328.65 237.19 82.78 Journal of Biogeography 35, 711–723 ª 2007 The Authors. Journal compilation ª 2007 Blackwell Publishing Ltd A topography-based tree line model which was 84.0%, was increased very little (< 0.05%) by the inclusion of the last two variables in the stepwise regression (Table S1). The significance of these variables was probably inflated because of the spatial dependence of the data points. We therefore used the complete model (last step of the stepwise regression) for prediction, but not for the assessment of the importance of the variables. The importance of the individual variables could be derived from the complete model only for uncorrelated and strongly contributing variables. Altitude was clearly the main factor determining tree line position; a model including only altitude correctly predicted forest cover in 80% of the training pixels (Table S1). Exposure differences between west and east slopes (eastness) were more important than those between north and south (northness); forest cover was higher on western slopes than on any other aspect (Fig. 4). The importance of the correlated variables (slope, CTI, PRR and STCI) was derived from the stripped models, which included only one correlated variable at a time (Table S2). Of these correlated variables, wetness (CTI) best predicted forest cover, with high wetness indicating low forest cover. This observation reflected the absence of forest in broad valley bottoms. The model reproduced these forest-free valley bottoms, but the modelled areas were smaller than the real (classified) forest-free areas (Figs 5b and 6). Although multicollinearity is not supposed to affect the non-correlated variables, we saw a reversal of the importance and the direction of some variables when including different correlated variables (Table S2). In particular, the roles of plan and profile curvature were reversed when including slope, PRR or STCI instead of CTI. With CTI included, convex curvatures predicted low forest cover, whereas with any of the other variables concave curvatures predicted low forest cover. We interpreted this as follows: CTI was low on ridges (convex landforms), so CTI predicted that all ridges are covered with forest. To compensate, convex curvatures predict lower forest cover. In contrast, slope, PRR or STCI could not accurately predict the absence of forest in valley bottoms, and if one of these variables was included in the model instead of CTI, concave curvatures (valley positions) predicted lower forest cover. The topographic variables that appeared to have a real effect on forest distribution were thus altitude, CTI, and eastness, in that order. In the model trained on test area A, the same variables were indicated to be most important (Table S3), but in the model trained on test area B, altitude had a more dominant effect and the next most important variable was profile curvature. However, multicollinearity was strong in both test areas for the same variables as in the training area (slope, PRR, CTI, STCI), so the importance of these correlated variables cannot be derived with certainty from these models. Again we explored the effect of including only one correlated variable at a time in stripped models, which confirmed the likeness of the pattern in test area A to the training area, and the dominance of altitude relative to all other variables in test area B. (a) 340 350 330 320 310 300 290 280 West North 10 20 70 30 60 40 50 50 40 60 30 70 20 80 10 East 0 260 100 250 240 230 220 210 200 190 (b) 340 350 330 320 310 300 290 280 West 110 South North 10 20 35 30 30 40 25 50 20 60 15 70 10 80 5 East 0 260 100 250 240 230 220 210 200 190 120 130 140 150 170 160 110 South 120 130 140 150 170 160 Figure 4 Aspect ecograms of the presence of forest on slopes (a) below and (b) above the average tree line altitude (3634 m). Shown is the percentage of the total number of pixels with a certain aspect where forest is present. Note the different scales on the radial axes. Model application The predictive accuracy of the complete model was high both in the training area (84.0%) and in the cross-validation area (83.3%). The specificity (percentage correctly predicted nonforest pixels) was somewhat higher (85.5% and 83.5%) than the sensitivity (percentage correctly predicted forest pixels: 82.4% and 83.1%). In test area A the predictive accuracy of the model was lower (69.7%), because of an over-estimation of forest cover throughout the area (Fig. 7a). So in this area, the specificity was very low (59.1%), whereas the sensitivity was very high (96.1%). In test area B the predictive accuracy was also lower Journal of Biogeography 35, 711–723 ª 2007 The Authors. Journal compilation ª 2007 Blackwell Publishing Ltd 717 M. Y. Bader and J. J. A. Ruijten (a) Figure 6 Predicted forest cover in the training and cross-validation area. 3-D view of the image shown in Fig. 5(b). 0 1 2 4 6 (72.4%), but in this area the over-estimation was more concentrated in certain locations, whereas in other locations forest cover was under-estimated (Fig. 7b). Specificity was again low (59.6%), whereas the sensitivity was higher (85.8%; Table S4). 8 km (b) DISCUSSION Forest distribution pattern 0 1 2 4 6 8 km Figure 5 (a) Predicted forest cover in the training and crossvalidation area. Lighter squares of the checkerboard pattern are the training area, darker squares are the cross-validation area. The underlying Landsat image is displayed as a false-colour composite, so that vegetation is shown in red. The red slopes on the right are covered in forest, the smaller red area on the left is a cultivated valley. The classification result of the Landsat image is shown only inside the tree-line zone (¼ training and cross-validation area), where pixels classified as forest are shown in red. (b) Difference between predicted forest cover and the real forest cover (classified from the Landsat image) in the training and cross-validation area. Inside the tree line zone, blue indicates areas where forest is predicted where in fact forest was not present, yellow indicates areas where no forest is predicted where in fact forest was present, red indicates correctly predicted forest, and the remaining transparent areas where the underlying Landsat image is seen indicate where the absence of forest was correctly predicted. Overall classification accuracy in training area: 84.0%; in cross-validation area: 83.3%. 718 Clearly, tree line position does not fluctuate randomly around an elevational contour line but depends on other topographic variables in a predictable way. After altitude, the most important variables were CTI (wetness index) and eastness. The strong effect of the wetness index in the model is mainly caused by the absence of forest on the flat bottoms of glacial valleys, where water tends to accumulate and soils are often waterlogged. This pattern, resulting in ‘inverted’ tree lines, is common in U-shaped valleys in mountains worldwide (Wardle, 1985; Young, 1993; Miehe & Miehe, 1994). Apart from accumulating water, such valley bottoms also accumulate cold air at night, which drains from the higher slopes and lies in these flat areas (Wardle, 1985; Sarmiento, 1986). Water and frost accumulation patterns in a landscape are often very similar (Blennow, 1998). The reason for the absence of trees in these valley bottoms may therefore be either waterlogging or low night temperatures, or a combination of both. The strong effect of eastness in the model is caused by the higher position of tree lines on western slopes than on eastern slopes. Note that this pattern occurs within the east-oriented, Amazonian slopes of the Andes, at a more local scale than the general lowering of tree lines on the Amazonian slopes compared with the drier inter-Andean slopes. The local difference between eastern and western slopes is probably caused by the difference in solar radiation received. As in many tropical mountains, a typical day in our study area has a clear morning and a cloudy and often rainy afternoon, followed by a clear evening (Smith & Young, 1987; Luteyn et al., 1999; Poveda et al., 2005). As a result, eastern slopes tend to receive Journal of Biogeography 35, 711–723 ª 2007 The Authors. Journal compilation ª 2007 Blackwell Publishing Ltd A topography-based tree line model (a) 0 1 2 4 6 8 km (b) 0 1 2 4 6 8 km Figure 7 Difference between predicted forest cover and the real forest cover (classified from the Landsat image) in test areas A (a) and B (b). The underlying Landsat image is displayed as a falsecolour composite. Inside the tree line zone, blue indicates areas where forest is predicted where in fact forest was not present, yellow indicates areas where no forest is predicted where in fact forest was present, red indicates correctly predicted forest, and the remaining transparent areas where the underlying Landsat image is seen indicate where the absence of forest was correctly predicted. Overall classification accuracy in test area A: 69.7%; in test area B: 72.4%. more solar radiation than other exposures (Sarmiento, 1986). Excess radiation, especially when preceded by low night temperatures, can cause photoinhibition in maladapted plants (Ball et al., 1991; Germino & Smith, 1999). Eastern slopes do not only receive more radiation, but they receive this radiation in the morning, directly after the cold night, when plants are most vulnerable. Seedlings of most cloud-forest tree species appear to be sensitive to such cold-induced radiation damage (Bader et al., 2007b), which may explain why these trees have difficulties establishing outside the forest, particularly on eastern slopes. Slowness of forest extension resulting from excess radiation may therefore have caused the observed lower tree lines on these slopes. Other conditions that may differ between eastern and western slopes are wind, moisture, and temperature. The higher radiation received by eastern slopes may result in drier conditions and higher temperatures (Smith, 1977; Azócar & Monasterio, 1980). On the other hand, although cloudiness is not expected to differ significantly between slopes at this scale, the eastern slopes are exposed to the prevailing winds coming up from the Amazon Basin and may receive more wind-driven moisture, resulting in windier and wetter conditions (Cavelier & Goldstein, 1989). We do not know the relative influence of these factors, and unfortunately no supporting climatic field measurements are available for this region. In our study area, an excess of moisture is more likely than a lack of moisture, but in well-drained positions this should not impair forest growth. Wind may be strong during storms, but is generally gentle, as on most tropical mountains (Bruijnzeel & Veneklaas, 1998). Temperatures may be higher on eastern than on western slopes, because more radiation is received (Azócar & Monasterio, 1980; Sarmiento, 1986), but higher temperatures would not depress the tree line (Körner & Paulsen, 2004). Therefore, we maintain that the most important reason for the lower tree lines on eastern slopes is probably radiation damage to young trees, but this issue needs further research. The small effect of northness on forest distribution was to be expected in this tropical region. The small effect of PRR is probably caused by the difference between this potential radiation and the actual radiation when cloudiness is taken into account. Clouds are especially frequent on the eastern slopes of the Andes, and changes in cloudiness through the day strongly affect the actual distribution of radiation (Bendix et al., 2006b) and hence the distribution of forest. Model application Whether the position of a tree line is determined by climate or is anthropogenically lowered is often unclear for a particular location. In many tropical mountain ranges it may be impossible to find an undisturbed training area against which potentially disturbed areas can be compared (Miehe & Miehe, 1994). In such cases, a pragmatic solution is to train the model in the least-disturbed area known in the region and use this best-we-have pattern as the standard to detect differences. These differences may indicate anthropogenic disturbances, but they could also point to variations in other environmental conditions. Because of the rather remote situation, our training area is presumed to experience limited human influence. However, we have no certainty about this, so it is safer to consider forest distribution in this area as a best-we-have pattern, rather than as being completely natural. In test area A, which we presumed also to be little disturbed, the model over-predicted the forest distribution all along the Journal of Biogeography 35, 711–723 ª 2007 The Authors. Journal compilation ª 2007 Blackwell Publishing Ltd 719 M. Y. Bader and J. J. A. Ruijten tree line. Still, a model trained in this area showed the same importance of variables as the models from the training area, which agrees with the even distribution of the over-prediction. If disturbances were responsible for the relative lack of forest, we would expect more localized effects and an alteration of the relationship with the topography. It therefore seems that these tree lines are lower than those in the training area because of climatic factors rather than because of human disturbances. The valleys in this area mostly start on the slopes of the snow-capped El Altar volcano (5319 m). Temperatures at a given elevation may therefore be unusually low owing to nocturnal cold-air drainage. Moreover, cloudiness may be high here, causing lower temperatures, but, according to the 3-year NOAA-AVHRR data presented by Bendix et al. (2006a), cloud frequency does not differ notably between our three study areas. Test area B, which we presumed to be disturbed, at least locally in the proximity of Atillo and Ozogoche, also had a lower tree line than the training area, as seen in the overestimation of forest cover by the model. In this case, the overestimation was less evenly distributed in the area than it was in test area A. Moreover, the model trained on test area B indicated a different relationship with the topographic variables than that in the training area. Again, we cannot exclude climatic reasons for the lower tree line; however, the location of the largest over-estimations might indicate a humaninduced lowering of the tree line that warrants further investigation. The patterns of forest distribution caused by human land use can be very similar to the patterns caused by natural processes and may therefore be hard to distinguish. For instance, the lack of forest on valley floors could theoretically also be caused by preferential human settlement in flat areas (Wardle, 1985), and tree lines could be lowered on eastern slopes owing to stronger fires if the slopes are drier, or owing to agricultural benefits if they are warmer (Smith, 1977). After identifying interesting locations, the real history of these sites can therefore only be studied in the field, for instance by determining the local land use or by reconstructing vegetation history based on local proxies, such as macroscopic charcoal (Di Pasquale et al., in press). It should be mentioned that this modelling approach is not the most appropriate approach if changes resulting from contemporary disturbances are studied, for instance the effects of the new Guamote–Macas road through Atillo and test area B. In such a case it is much more accurate and simpler to compare the actual forest distribution on remotely sensed images from before and after road construction. Methodological issues Classification At the local scale, tree lines are ecotones of varying width, having spatial patterns ranging from abrupt boundaries, through tree-height or tree-density gradients, to mosaics of 720 vegetation patches (Wardle, 1965; Körner, 1998; Bader et al., 2007a). Zooming out, the tree line starts to look more and more like a crisp boundary. In the section of the study area that we visited, the transition zone was narrow, less than 30 m, so at the scale of a Landsat image (30-m pixels) this tree line was abrupt and could be considered a line. We cannot, however, exclude the possibility that in other parts of the study areas a broader transition zone was present, as in some remote areas of nearby Llanganates National Park (R. Hofstede, personal communication, 2006). In our method, such zones of shrubs and forest patches would be classified as forest, so that the tree line is defined as the upper boundary of the tree line ecotone. For an analysis of the spatial pattern within the ecotone, which can indicate land-use effects or natural vegetation processes, a classification with more classes and data with a higher spatial resolution are needed (Wiegand et al., 2006; Bader et al., 2007a). Spatial resolution Small forest patches in the páramo, even when discernable on the Landsat image, cannot be explained by the topography because of the lower DEM resolution (90 m) and had to be excluded from the analysis. A model based on these data can therefore only describe coarse-scale patterns and indicate prevailing environmental conditions, even if in the field there can be considerable variability owing to smaller topographic features. This problem occurs at all scales, and the most suitable scale of investigation should ideally be based on the goals of the study, although the availability of data is also an important criterion in practice. If the main goal of the model is to detect human disturbances, the current scale is sufficient if coarse-scale impacts are of concern. If the main goal is to understand the processes that cause the tree line, the current scale is sufficient to reveal some important limitations for forest growth, as shown in this study. Nevertheless, patterns caused by other limitations may only be discernable at a more detailed scale. Spatial accuracy The DEM, as well as the Landsat image, had limited spatial accuracy, resulting in some displacements of forest cover relative to the topography. As long as the errors in both data sets are randomly distributed, they will weaken the effect of topographic variables in the logistic model, but they will not lead to any false positive conclusions. However, systematic errors may cause relationships in the model that are not related to relationships in the terrain. In the Americas, the SRTM DEM appears to contain an over-estimation of the altitude of northern to eastern slopes (Jarvis et al., 2004; Rodriguez et al., 2005). This could lead to a model that falsely indicates that tree lines are higher on these slopes. However, our models indicated that tree lines were higher on western slopes, and we can therefore be confident that this relationship is not an artefact of systematic errors in our data. Journal of Biogeography 35, 711–723 ª 2007 The Authors. Journal compilation ª 2007 Blackwell Publishing Ltd A topography-based tree line model The 16% forest cover that could not be explained by topographic variables may be attributable to random natural variation or to the effects of processes not related to the topography or not captured in the topographic variables used, for instance rock type and disturbances. Moreover, the model includes only linear relationships and no interactions between variables, simplifications that have probably resulted in a lower fit of the model. In addition, the model fit will be lower because of the spatial inaccuracies in the data and the low resolution of the DEM. 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SUPPLEMENTARY MATERIAL The following supplementary material is available for this article online: Table S1 Classification tables showing the predictive accuracies of the models of each of the steps of the forward stepwise logistic regression in the training area. Table S2 Results of forward stepwise regressions (model coefficient (B), S.E., and change in )2 log likelihood) including only one of the correlated variables per regression (the stripped models). Table S3 Results of forward stepwise regressions (model coefficient (B), S.E., and change in )2 log likelihood) for test areas A and B. Table S4 Classification tables showing the predictive accuracies of the complete model in the training and cross-validation areas and in test areas A and B. This material is available as part of the online article from: http://www.blackwell-synergy.com/doi/abs/10.1111/j.13652699.2007.01818.x Please note: Blackwell Publishing is not responsible for the content or functionality of any supplementary materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article. BIOSKETCHES Maaike Bader is an ecologist studying spatial and temporal vegetation patterns and their causes and dependence on functional plant traits, using field experiments and theoretical models. She recently finished her PhD project on tropical alpine tree lines. Johan Ruijten is a specialist in geo-information science and remote sensing, with a special interest in ecological applications. Editor: Mark Bush Journal of Biogeography 35, 711–723 ª 2007 The Authors. Journal compilation ª 2007 Blackwell Publishing Ltd 723